The use of "program" and "programme" is one of the most common confusions I encounter in proofreading. One of the reasons it is so common is because of the increasing intrusion of US spelling, which uses "program" differently from UK spelling.
The rules governing "program" and "program" in UK spelling are:
Use "programme" except when referring to computer software, in which case it is "program".
But in US spelling, French-based spellings from UK English, such as "programme", have been eliminated. So in US spelling, "program" is used in all contexts of "programme" and not just when referring to computer software.
And what with US spelling becoming increasingly frequent on the Internet and being used as default language on computers, it is not surprising that Americanisms are permeating non-US English and leading to what would be spelling errors in UK spelling. One such is incorrect use of "program" when it should be "programme", and I have seen this in many walks of public life.
However, what was once incorrect can become increasingly acceptable. For example, the American "z" spelling is becoming more acceptable, although "s" spelling is still more traditional and correct in UK spelling. Indeed, the American use of "program" has been accepted in Australian spelling - something I must always bear in mind when I proofread a document that uses such spelling. So it is possible that the use of "program" will eventually overtake "programme" in UK spelling as well. But in the meantime, the traditional use of "programme" and "program" stands in UK spelling.